Question

The perimeter of a rectangular plot is 62 m and its area is 228 sq metres. Find the dimensions of the plot.

Answer 1

$$\begin{gathered} \text{Let the length and breadth of the rectangular plot be}x\text{and}y\text{meter, respectively}\text{.} \\ \mathrm{Therefore},\mathrm{we}\mathrm{have}: \\ \text{Perimeter = 2}(x+y)=62...\left(\text{i}\right)\text{and} \\ \mathrm{A}\text{rea =}xy=228 \\ \Rightarrow y=\frac{228}{x} \\ \text{Putting the value of}y\text{in}\left(\text{i}\right)\text{, we get} \\ \text{⇒ 2}(x+\frac{228}{x})=62 \\ \Rightarrow x+\frac{228}{x}=31 \\ \Rightarrow \frac{x^2+228}{x}=31 \\ \Rightarrow x^2+228=31x \\ \Rightarrow x^2-31x+228=0 \\ \Rightarrow x^2-(19+12)x+228=0 \\ \Rightarrow x^2-19x-12x+228=0 \\ \Rightarrow x(x-19)-12(x-19)=0 \\ \Rightarrow (x-19)(x-12)=0 \\ \Rightarrow x=19\text{or}x=12 \\ \text{If}x=19\text{m},y=\frac{228}{19}=12\text{m} \\ \mathrm{Therefore},\mathrm{the}\mathrm{length}\mathrm{and}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{plot}\mathrm{are}19\mathrm{m}\mathrm{and}12\mathrm{m},\mathrm{respectively}. \end{gathered}$$